Try the following SAT math practice question (Calculator Permitted) that tests your understanding of algebraically manipulating exponent expressions.

**Question**(Calculator Permitted):

$$ (\sqrt{27})^{m} = \sqrt[3]{(81)^{n}} $$

If $m$ and $n$ are positive numbers in the equation above, what is the value of $\displaystyle \frac{m}{n}$ ?

- $\quad \displaystyle \frac{3}{4}$
- $\quad \displaystyle \frac{8}{9}$
- $\quad \displaystyle \frac{9}{8}$
- $\quad \displaystyle \frac{4}{3}$

**Video Explanation**